Rodriguez, who made the switch from Monaco this summer, made his first competitive appearance for the club in the 2-0 win over Sevilla in Wales.
"Not only to play with Cristiano [Ronaldo] but with all the stars, hopefully I can play with them a lot more," the Colombia international told reporters.
"I hope I can soon accomplish more with this great club. This is something unique I will never forget.
"It's been very fast but when one is mature everything is easier. I'll play wherever the coach wants - number eight, number 10, as a striker."
Rodriguez finished as the top scorer at this summer's World Cup.